DISTORTION DISTRIBUTION AND CONVERGENCE ANALYSIS OF SPHERICAL DIAMOND DISCRETE GRIDS
ZHOU Liang-Chen, LIN Bing-Xian, LV Guo-Nian, ZHAO Zhi-Peng Key Lab of Virtual Geographic Environment, MOE, Nanjing Normal University,
1, Wenyuan Road, Nanjing, Jiangsu Province, P R China, 210023 zhoulchgmail.com
KEY WORDS: Global Discrete Grid, Spherical Diamond Discrete Grid, Distortion Distribution, Convergence Analysis, Electrical
Potential Energy
ABSTRACT:
Four kinds of subdivision methods of Global Discrete Grid are presented in this paper. Furthermore, we systematically and comprehensively compare and analyze the distortion distribution and convergence of spherical diamond discrete grids. Especially,
the Electrical Potential Energy is introduced as index to measure the distortion distribution of spherical diamond discrete grids. The result shows that the properties including the distortion of the area of the grid cell and the distortion of the angle of the grid cell or
from the global uniformity of spherical diamond discrete grids which are obtained by recursively bisecting the great arcs on the surface of the globe starting with the icosahedron are much better than the properties of the other three discrete grid obtained by
subdivision methods.
1. INTRODUCTION
Spherical diamond discrete grids are more easily to search neighboring cells and build hierarchical relation, and more
suitable to manage global distributed massive spatial data and update local data dynamically, since their geometric structure is
similar to the structure of square grids on planar, their coding method is simpler than that of triangular grid or hexagon grid,
and they are oriental uniform and radially symmetrical. According to the basic polyhedron such as, octahedron,
icosahedron and recursive bisection method, foreign and domestic researchers have proposed several different methods
to construct spherical rhomboidal discrete grids which are all applied to manage and integrate the global multi-scale and
multi-resolution spatial data like great arc bisecting method, longitude and latitude bisecting method, mixed bisecting
method based on octahedron, and great arc bisecting method based on icosahedron. The applications based on octahedron
include a hierarchical spatial data structure for global geographic information systems Goodchild, 1922, continuous
indexing of hierarchical subdivisions of the globe BarthildiJ, 2001, spatial data quality and hierarchical comprehensive data
model Dutton, 1999; Gold, 2000;Li, 2003. The applications based on icosahedron are spherical hierarchical data index
Fekete, 1990, global navigation model Lee, 2000, geodesic discrete global grid system 2003, Sahr.
Getting spherical discrete grid, the geometrical characteristics of which is excellent and distortion distribution of which is
uniform, is major subject of the research of Digital Discrete Grid Goodchild, 2000. But from spherical geometry we know
there is a method by which we can get nearly the same instead of absolute the same geometrical characteristics such as, area,
length, and angle as the planar raster. Before making full use of spherical diamond discrete grids, we need to figure out the
questions, such as what’s the similarity, what’s the regulation of distribution of the area and angle, and are they converge, and
analysis the numerical error of the grid model.
2. GENERATION METHOD OF SPHERICAL
